I learn that Eaton's car was of the Yardley Team BRM. It can't be this one.
But your intuiton of a Brabham BT33 could be the most enlightened one, since Rolf Stommelen drove a BT33, under #12, [error!] Oops! In Canada 1970.

… No. It doesn't look like a BT33 whose nose is very characteristic.

… It looks like a McLaren. The trompettes d'admission are rather high. Maybe a F5000, like you said?